# MIT Probability Seminar

## Current Organizers

• Alexei Borodin
• Promit Ghosal
• Jimmy He
• Elchanan Mossel
• Philippe Rigollet
• Scott Sheffield
• Yair Shenfeld
• Nike Sun
• Dan Mikulincer
• Subscription to a mailing list

# Fall 2022

Monday 4.15 - 5.15 pm

Room 2-147

Scheduled virtual talks will be held on Zoom, Monday 4:15-5:15 pm.
A link to a Zoom classroom will appear here!!

## Schedule

• September 12

Room: 2-147

Guilherme Silva
Universidade de São Paulo (ICMC - USP)

Universality for a class of statistics of Hermitian random matrices and the integro-differential Painlevé II equation.

Abstract:

It has been known since the 1990s that fluctuations of eigenvalues of random matrices, when appropriately scaled and in the sense of one-point distribution, converge to the Airy2 point process in the large matrix limit. In turn, the latter can be described by the celebrated Tracy-Widom distribution.

In this talk we discuss recent findings of Ghosal and myself, showing that certain statistics of eigenvalues also converge universality to appropriate statistics of the Airy2 point process, interpolating between a hard and soft edge of eigenvalues. Such found statistics connect also to the integro-differential Painlevé II equation, in analogy with the celebrated Tracy-Widom connection between Painlevé II and the Airy2 process.

• September 19

*** Special Seminar Starting at 3pm! ***

Room: 2-132

Matteo Mucciconi University of Warwick

A bijective approach to solvable KPZ models

Abstract:

Explicit solutions of random growth models in the KPZ universality class have attracted, in the last two decades, significant attention in Mathematical Physics. A common approach to the problem, explored in the last 15 years, leverages remarkable relations between the KPZ equation and quantum integrable systems.

Here, I will introduce a new approach to the solutions of KPZ models, based on a bijection discovered by Imamura, Sasamoto and myself last year. This is a generalization of the celebrated Robinson-Schensted-Knuth correspondence relating at once 1) solvable growth models, 2) determinantal point processes of free fermionic origin and 3) models of Last Passage Percolation on a cylinder.

I will enumerate some of the early applications of this new approach and I will give an overview of the technical tools needed, that include Kashiwara's crystals or the inverse scattering method for solitonic systems.

• September 26

Room: 2-147

Abstract:

• October 3

Room: 2-147

Learning low-degree functions on the discrete hypercube

Abstract: Let f be an unknown function on the n-dimensional discrete hypercube. How many values of f do we need in order to approximately reconstruct the function? In this talk we shall discuss the random query model for this fundamental problem from computational learning theory. We will explain a newly discovered connection with a family of polynomial inequalities going back to Littlewood (1930) which will in turn allow us to derive sharper estimates for the the query complexity of this model, exponentially improving those which follow from the classical Low-Degree Algorithm of Linial, Mansour and Nisan (1989). Time permitting, we will also show a matching information-theoretic lower bound. Based on joint works with Paata Ivanisvili (UC Irvine) and Lauritz Streck (Cambridge).

• October 10

Room: 2-147

Abstract:

• October 17

Room: 2-147

Abstract:

• October 24

Room: 2-147

Hao Shen

Abstract:

• October 31

Room: 2-147

Robert Hough
Stony Brook University

Covering systems of congruences

Abstract:

A distinct covering system of congruences is a list of congruences $a_i \bmod m_i, \qquad i = 1, 2, ..., k$ whose union is the integers. Erdős asked if the least modulus $m_1$ of a distinct covering system of congruences can be arbitrarily large ( the minimum modulus problem for covering systems, $1000) and if there exist distinct covering systems of congruences all of whose moduli are odd (the odd problem for covering systems,$25). I'll discuss my proof of a negative answer to the minimum modulus problem, and a quantitative refinement with Pace Nielsen that proves that any distinct covering system of congruences has a modulus divisible by either 2 or 3. The proofs use the probabilistic method and in particular use a sequence of pseudorandom probability measures adapted to the covering process. Time permitting, I may briefly discuss a reformulation of our method due to Balister, Bollobás, Morris, Sahasrabudhe and Tiba which solves a conjecture of Shinzel (any distinct covering system of congruences has one modulus that divides another) and gives a negative answer to the square-free version of the odd problem.

• November 7

Room: 2-147

Abstract:

• November 14

Room: 2-147

Sven Wang
MIT

Abstract:

• November 21

Room: 2-147

Emma Bailey
City University of New York (CUNY)

Abstract:

• November 28

Room: 2-147

Sayan Das
Columbia University

Abstract:

• December 5

Room: 2-147

Changji Xu
Harvard University

Abstract:

• December 12

Room: 2-147

Hoi Nguyen
The Ohio State University

Abstract: